Tuning of Search of the Problem Space for Geometry Proofs

Abstract

In planning a proof, a student searches through a space of inferences leading forward from the givens of the problem and backward from the to-be-proven statement. One dimension of growth of expertise is that students become more tuned in the search of this problem space. This can be shown to result from the application of various learning operators to production embodiments of the inference rules. Rules are evaluated after the solution of a problem according to whether they led to or led away from the solution. Rules that contributed to a solution are strengthened and an attempt is made to formulate general versions of these rules that w i l l apply in other situations. Rules that led away from the solution are weakened and a discrimination process is evoked to try to add features to the rules that w i l l try to restrict them to the correct